To estimate square roots, you will find what perfect squares it is in between. For example, the number 51 would be between 7 and 8, as it is in between 49 and 64. Then you will keep on making estimations to the hundredth on the calculator and see which is closest.
40 is in between 6 and 7, and is probably found near the beginning or middle. Let's estimate a bit.
6.5²=42.25 6.4²=40.96 6.3²=39.69
The first two digits of are 6.3, as it is the closest number to 40. 6.4 was close as well, so the hundredths digit will probably be found in the beginning/middle again.
6.35²≈40.32 6.33²≈40.06 6.32²=39.94
The best estimation for √40 is about 6.32. ----------------------------------------------------------------------------- For the next few questions I will just show you the work.
8.5²=72.25 8.6²=73.96 8.7²=75.69
8.7 is closest, but we cannot get it to go backwards. We will switch to 8.6 to get it closer, and select the middle/end numbers.
8.65²≈74.82 8.66²≈75
Our estimation for √75 is 8.66. ------------------------------------------------------------------------- 9.5²=90.25 9.4²88.36
9.5² is the closest to 90, but we cannot add hundredths to make it smaller. We will use 9.4 and use larger hundred digits.
9.49²≈90.1
Our estimation for √90 is 9.49. ----------------------------------------------------------- 15.5²=240.25 15.6²=243.36 15.7²=246.49
I believe our best estimation for√245 is 15.65 ----------------------------------------------------------------------------------------- 21.5²=462.25 21.4²=457.96 21.3²=453.69 21.2²=449.44
21.2 seems like the best number to continue on with.
21.23²≈450.71 21.22²≈450.29 21.21²≈449.86
Our estimation for√450 is 21.21. ------------------------------------------------------------------------ 25.5²=650.25 25.4²=645.16 25.3²=640.09 25.2²=635.04
25.3 is just above 40, but we need to have a hundredths place. Therefore, we will select 25.2.
25.29²≈639.58
Our estimation for √640 is is 25.29. ------------------------------------------------------------------------------- 25.5²=650.25 25.7²=660.49 25.9²=670.81
As 25.9 is just a bit over 670, we will use 25.8
25.89²≈670.29 25.88²=669.77
Our estimation for √670 is 25.88. -------------------------------------------------------------------- Our estimations for each question are seen below. √40≈6.32 √75≈8.66 √90≈9.49 √245≈15.65 √450≈21.21 √640≈25.29 √670≈25.88
Answer: When there are two of the same signs when adding and multiplying it means they are positive but two of the same are negative, which means Clara is rights.
